The clutch oil pressure (P cl ) supplied to a hydraulic control apparatus of an automatic transmission is detected. If it is detected that the clutch oil pressure (P cl ) is less than or equal to a first threshold value P A when a first oil pump cooperative with a drive power source is to stop, the second oil pump is driven. Therefore, after the oil pressure (for example, P y ) remaining due to the first oil pump has decreased, the second oil pump is driven, and an oil pressure (P x ) needed for the hydraulic control of friction engagement elements is maintained. If it is detected that the clutch oil pressure (P cl ) is greater than or equal to a second threshold value (P B ) when the first oil pump is to be driven, the second oil pump is stopped. Therefore, the second oil pump is stopped when the oil pressure provided by the first oil pump rises to such a level that the oil pressure (P x ) can be secured. Thus, the load on the second oil pump is reduced so as to allow a size reduction thereof.